# I What is saturation magnetization

1. Apr 10, 2017

### Belhazred

Hi guys,

I recently performed an experiment, in which I found the B-H hysteresis loops for four ferromagnetic materials. I've attached a graph of my results for one alloy in the link below, where the labels are the saturation magnetization for each driving voltage.

http://imgur.com/a/2H246

My question is: why are there four different values for the saturation magnetisation, when online values are often quoted as a single value? The B-H loop was acquired by placing the material inside a solenoid, and driving a sinusoidally varying voltage of 1-4 amps at a frequency of 1Hz through the coils.

Is there any way to link the driving voltage to the applied magnetic field? Like in this graph: https://commons.wikimedia.org/wiki/File:B-H_loop.png.

Any help would be appreciated!

2. Apr 10, 2017

### ZapperZ

Staff Emeritus
Back up a bit.

You have 4 different ferromagnetic materials, am I right?

So why should they all have the same saturation under the identical experimental settings? Where do you read that all ferromagnetic materials should have just one definite saturation value?

Zz.

3. Apr 10, 2017

### Belhazred

Hi,

Sorry for not clarifying, yes i have four different ferromagnetic materials. However for each material, I am obtaining a range of values for the saturation magnetization (shown in the graph). I found expected saturation values from this article http://coefs.uncc.edu/mnoras/files/2013/03/Transformer-and-Inductor-Design-Handbook_Chapter_2.pdf. My range of values seems to be smaller than theirs; I suspect this may be related to the driving voltages which were used, but I don't know why, hence the confusion :)

4. Apr 10, 2017

### ZapperZ

Staff Emeritus
But aren't those different curves done when you applied different amplitude to the external current? You really have not obtained the saturation field yet with those smaller amplitudes.

Zz.

5. Apr 10, 2017

### Belhazred

Yes that's correct. So for the smaller amplitudes, i can say that saturation magnetisation has not been reached. However, for 3-4 V, I have values for saturation magnetisation for each respective voltage; which one do I use, or do I say that saturation is within the range of the values that I obtained? Why does increasing the applied amplitude to the external current increase the saturation magnetisation? I thought that when all the domains in a material are alligned, saturation is reached; so how can increasing the external field increase the saturation magnetisation given that there are only a finite amount of domains to 'allign'. Apologies if i am being unclear, my knowledge of the subject isn't the best =p

6. Apr 13, 2017

### nasu

No, you don't have saturation magnetization for each voltage. From the look of your curves, it may be that none of them reaches saturation.

And, as as you plot B versus H, the values picked from the graph are values of B and not of magnetization. If you plot M vs H, at saturation the curve becomes a horizontal line. If you plot B vs H the line is not horizontal but has some non-zero slope due to the contribution of the external field to B. In order to get magnetization you could extend the line until it crosses the B axis. The intercept is equal to $$\mu_0 M_s$$ if you use SI units (In Si units we have $$B=\mu_0 H + \mu_0 M$$ and at saturation M is constant).

7. Apr 13, 2017

### Belhazred

Hey Nasu,

Thanks for responding, that makes sense. I plotted M versus H for all the metals tested. You can see an example here: http://imgur.com/a/4eQen.
The hysteresis loops are there, but don't become horizontal lines... Maybe a higher driving voltage would be needed to see this effect?